Prime Factorization Calculator
One integer per line - factor it into primes with exponent form, divisor count and divisor sum
Output:
Separator:
Calculation Result
Download CSV
| No. | Original | Factorization | Exponent form | Divisors | Sum of divisors |
|---|
Introduction to the tool and how to use it
Prime factorization calculator splits integers into a product of primes, one number per line, with batch paste supported.
For example, 360 = 2 × 2 × 2 × 3 × 3 × 5 = 2^3 × 3^2 × 5, with 24 divisors and a divisor sum of 1170.
The algorithm uses BigInt: small factors are first stripped using primes below 1000, then Miller-Rabin checks primality and Pollard rho splits composites; composites up to 18 digits are factored quickly. Composites that are too large to factor are skipped with a notice, so no wrong result is returned.
For example, 360 = 2 × 2 × 2 × 3 × 3 × 5 = 2^3 × 3^2 × 5, with 24 divisors and a divisor sum of 1170.
The algorithm uses BigInt: small factors are first stripped using primes below 1000, then Miller-Rabin checks primality and Pollard rho splits composites; composites up to 18 digits are factored quickly. Composites that are too large to factor are skipped with a notice, so no wrong result is returned.
How to use
- Enter one integer per line, such as
360. - Choose the output format (product plus exponents / product only / exponents only).
- Click Start calculation; the result table shows both notations, divisor count, and divisor sum, with one-click copy and CSV export.
Factorization
Prime factorization of 360
360 = 2^3 × 3^2 × 5, which is 2 × 2 × 2 × 3 × 3 × 5 written out in full.
- Exponent form2^3 × 3^2 × 5
- Product form2 × 2 × 2 × 3 × 3 × 5
- Divisor count24
- Divisor sum1170
Divisor list
| # | Divisor | Paired divisor |
|---|---|---|
| 1 | 1 | 360 |
| 2 | 2 | 180 |
| 3 | 3 | 120 |
| 4 | 4 | 90 |
| 5 | 5 | 72 |
| 6 | 6 | 60 |
| 7 | 8 | 45 |
| 8 | 9 | 40 |
| 9 | 10 | 36 |
| 10 | 12 | 30 |
| 11 | 15 | 24 |
| 12 | 18 | 20 |
| 13 | 20 | 18 |
| 14 | 24 | 15 |
| 15 | 30 | 12 |
| 16 | 36 | 10 |
| 17 | 40 | 9 |
| 18 | 45 | 8 |
| 19 | 60 | 6 |
| 20 | 72 | 5 |
| 21 | 90 | 4 |
| 22 | 120 | 3 |
| 23 | 180 | 2 |
| 24 | 360 | 1 |
- Divisors are listed in ascending order; the paired divisor is the one it multiplies with to give the original number.
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